Major changes in this edition include the substitution of probabilistic arguments for combinatorial artifices, and the addition of new sections on branching.

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In our study, the weak Fe-Ni-S alloy is oriented almost parallel to the shear plane. This difference is most likely related to the substantial amount of axial compressive stress that the samples undergo before and during deformation in simple shear. Let us consider effects of PSC and shear-induced texture development on the rheological properties of the lower mantle. For simplification, we assume the mantle consists of silicate perovskite Pv and ferropericlase Fp only. A number of observations suggest that Fp is the weaker phase Weaver, ; Hulse et al.

When discussing mantle dynamics, it is more convenient to use viscosity, which, for solids, is proportional to the ratio of strength to strain rate, than the strength alone. Using experimentally measured diffusion coefficients and homologous temperature scaling, Yamazaki and Karato calculated that the viscosity of Pv is about three orders of magnitude higher than that of Fp. Figure 11 shows one attempt to estimate the rheological properties of the lower mantle and the effects of texture on bulk viscosity.

Based on the rheological properties for Pv and Fp given by Yamazaki and Karato , their Table 1 , viscosities are estimated for depths of and km using the approach outlined by Takeda Here we adopt a lower mantle geotherm with a temperature gradient of 0. For each depth, the upper line represents viscosities for the ideal LBF texture, whereas the lower curve corresponds to viscosities for the ideal IWL texture Takeda, ; Yamazaki and Karato, Thus, once the transition from LBF to IWL occurs, bulk viscosity will suddenly decrease from the upper curve to the lower one.

We examine a cross section from the edge of the subducting slab point A to the edge of the upwelling conduit point B , at a constant depth of, e. These shear zones are also thermal boundary layers: temperatures adjacent to the downwelling and upwelling conduits may be a few hundred Kelvin cooler and hotter, respectively, than the ambient mantle Fig. Figure 12C gives the likely deformation mechanisms of different regions along the cross section.

As a result, the viscosity along the flow direction is dominated by that of Fp Fig. Hence, dynamic processes are likely controlled by the rheological properties of Fp. Texture-induced rheological weakening may have profound effects on the dynamics of a subducting slab. A slab penetrating into the lower mantle introduces large deformation in the surrounding mantle, especially around the tip of the slab.

The mantle material undergoes a textural transition to adapt an IWL fabric, and the effective viscosity decreases. The magnitude of this decrease in effective viscosity may range from to , resulting in an avalanching enhancement for the downwelling process. Measurements of the rheological properties of Pv and a full understanding of dominant deformation mechanisms under various pressure, temperature, grain-size, and strain-rate conditions are required to evaluate the effects quantitatively.

Development of an IWL fabric is also associated with seismic anisotropy.

A simple estimate, based on an IWL-induced, weak, transversely anisotropic composite e. LPO associated with the texture may further enhance the degree of anisotropy. Future high-resolution seismic studies may be able to resolve the contributions of anisotropy caused by this shear zone from that within the slab. We have developed a new experimental technique, called HPXTM high-pressure X-ray tomography microscope , to study the mechanical properties of multiphase materials.

Stress measurements were not performed at this stage of the development; however, by implementing a multi-element detector and conical slits e. Further improvements in optical components such as scintillator materials and cameras and mechanical components will be sought to increase spatial resolution. Two types of starting samples were studied: an LBF-type texture, where the alloy phase was present as isolated spherical inclusions, and a near-IWL-type texture, where the alloy phase was concentrated near grain boundaries and tended to form an interconnected network.

Results indicate that regardless of the initial texture, large shear deformation causes a dramatic texture transition from LBF to IWL, the alloy phase forming laminated layers subparallel to the shear plane. For such a laminated IWL texture, effective rheological properties should be dominated by the weak phase.

Our results indicate that the deformation mechanisms in the strong matrix material silicate in our study play a less important role in the development of the IWL fabric than does the contrast in rheological properties between the constituent phases. In addition, the observed texture transition should be a common phenomenon in rock assemblies with high phase-strength contrast. The regions most likely to be affected are within the thermal boundary layers adjacent to subducting slabs, where a strong IWL texture is expected to develop, thereby greatly reducing the bulk viscosity in these regions.

This scenario should be considered in geodynamic models. Also, since lamination develops in planes subparallel to the flow direction, SPO-induced elastic anisotropy will also develop in the composite. A simple model indicates that in these highly deformed regions, SPO-induced anisotropy may be as much as 0. Seismic studies on anisotropy may provide the clues researchers need to infer the degree of deformation and, hence, the rheological weakening in the lower mantle. We are grateful to G. Karato for his valuable comments on early versions of the manuscript.

We also thank two anonymous reviewers, whose thorough and constructive reviews significantly improved the manuscript. Use of the Advanced Photon Source was supported by the U.

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Work by J. Roberts was performed under the auspices of the U. Backscattered electron image of sample A, as synthesized. Light gray areas are spherical Fe-Ni-S inclusions. The brighter contrast in these inclusions was caused by quenching the near-eutectic composition during melting. Fine, brighter regions are almost pure Fe-Ni, and darker regions are close to FeS in composition.

The darker background contains two types of grains. Large euhedral grains with homogeneous appearance are enstatite En ; the darkest, complex areas are intergrowths of quenched melt m with compositions close or slightly more Mg-enriched than olivine. Also note the tiny Fe-Ni-S spherical inclusions three arrows that appear only in the complex, olivine-like grains. Inset shows the contrast between the two silicate regions. Backscattered electron images of sample B, as synthesized. Bright areas are Fe-Ni-S quenched melts, which appear along grain boundaries of the silicate pure olivine in this case.

Some melts appear to form channels arrow in B. In B, many olivine grain boundaries show tubular channels, presumably caused by losing Fe-Ni-S during polishing. A schematic illustration of the cell assembly used in the high-pressure—high-temperature tomography experiments. Units are in millimeters. BN—boron-nitride; WC—tungsten carbide. Strain markers and determination of maximum shear strain during deformation at high pressure and high temperature. A Illustration of the locations of the markers examined: a pair of Fe-Ni-S inclusions, one at the top viewed from above and the other at the bottom viewed from below of the sample, is located near the cylindrical surface, and then their relative rotation is determined.

From this angle, the radius and the total height of the sample also imaged and the maximum shear strains are determined. B—H The locations of the marker pair left: top; right: bottom at various twist angles. In C, the white arrows indicate the direction of shear. Fe-Ni-S inclusions extracted from a series of tomographic images using Blob3D see text.

Top row shows complete images of the sample when the silicate matrix is removed; bottom row shows examples of the inclusions extracted. A Ambient sample before compression. B Sample loaded to 3 GPa, at room temperature. C Sample loaded to 6 GPa after heating to K. Note that because of resolution limitations and because Blob3D treats each inclusion as an ellipsoid, very small inclusions cannot be imaged properly.

For each pair, the upper image e. Three-dimensional tomographic reconstruction of sample B at 1 GPa and room temperature before heating and shear deformation. The starting view is along the sample axis. The view is about one-quarter of the circular cross section. S1 or the full-text article on www. Three-dimensional tomographic image of sample B at 3. Similar view as in Animation 1.

S2 or the full-text article on www. Rose diagram pairs for the star volume distribution analyses. Top row shows the rose diagrams in sample radial directions. In the bottom row, Up and Down indicate the sample axial direction. Note the gradual disappearance of the horizontal shape-preferred orientation as the sample was sheared top row, from left to right and the significant flattening of the inclusions bottom row, from left to right. Virtual thin sections from tomographic images for sample A.

A Ambient condition, before compression. B 6 GPa, room temperature rm T , before heating. C—I After heating to K and twisting at various angles. Values in parentheses are twisting angle and shear strain. Bright contrasts are Fe-Ni-S inclusions imaged. Note the development of linear features as shear strain increases.

Large Deformation of Materials with Complex Rheological Properties at Normal & High Pressure

The initial horizontal dimension A is 1 mm. Backscattered electron images of sample A A and sample B B , recovered after the high-pressure—high-temperature tomography experiment. Sample A can be directly compared with the last virtual thin section in Figure 7. High-pressure—high-temperature tomography has captured most of the features.

The rotating axis is vertical for torsional shear generation. Three-dimensional tomographic image of sample A after recovery from the high-pressure—high-temperature shear deformation experiments. Images collected at Advanced Light Source. S3 or the full-text article on www. Backscattered electron images of sample A at higher magnifications. A Alloy lenses appear in the silicate matrix.

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Backscattered electron images of sample B. A Thin lamination is well developed in planes nearly perpendicular to the loading axis parallel to the shear plane. B The olivine matrix also underwent significant grain-size reduction. In places, the original large grain can still be recognized. Adjacent small grains have close crystallographic orientations. The upper bound corresponds to the idealized LBF load-bearing framework fabric and the lower bounds to the idealized IWL interconnected layers of the weaker phase fabric.

For SVD, these lines are considered infinitesimal cones, with their vertex the analysis direction vertex at the origin point and subtending a solid angle as they approach the material interface. Supplementary data. Figure 1. View large Download slide. Animation 1. Animation 2. Animation 3. TABLE 1. Volume 7, Number 1. Previous Article Next Article. View Full GeoRef Record.

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Computation of linear elastic properties from microtomographic images: Methodology and agreement between theory and experiment. Search ADS. Plastic deformation and development of clinopyroxene lattice preferred orientations in eclogites. Analogue experiments and numerical modelling on the relation between microgeometry and flow properties of polyphase materials. Experimental investigation into the microstructural and mechanical evolution of phyllosilicate-bearing fault rock under conditions favouring pressure solution. Anisotropic parameters of layered media in terms of composite elastic properties.

An interconnected network of core-forming melts produced by shear deformation. The strength of Mg 0. Textural and mechanical evolution with progressive strain in experimentally deformed aplite. Anisotropic viscosity of a dispersion of aligned elliptical cylindrical clasts in viscous matrix. The effect of particle shape and stiffness on the constitutive behavior of metal-matrix composites. Flow laws for rocks containing two non-linear viscous phases: A phenomenological approach.

Mechanisms of weak phase interconnection and the effects of phase strength contrast on fabric development. Competence contrasts in ductile deformation as illustrated from naturally deformed chert-mudstone layers. Seismic anisotropy in the deep mantle, boundary layers and the geometry of mantle convection. Diffusion creep in perovskite: Implications for the rheology of the lower mantle. Superplasticity in Earth's lower mantle: Evidence from seismic anisotropy and rock physics. Shear deformation of dry polycrystalline olivine under deep upper mantle conditions using a rotational Drickamer apparatus RDA.

Computational rock physics: Transport properties in porous media and applications [Ph. Three-dimensional grain fabric measurements using high-resolution X-ray computed tomography. Computational methods for quantitative analysis of three-dimensional features in geological specimens. Acquisition, optimization and interpretation of X-ray computed tomographic imagery: Applications to the geosciences. Shearing melt out of the Earth: An experimentalist's perspective on the influence of deformation on melt extraction.

Deformation mechanisms in experimentally deformed single crystals of pyrrhotite, Fe1—xS. A model for composites containing three-dimensional ellipsoidal inclusions. Volumetric properties of magnesium silicate glasses and supercooled liquid at high pressure by X-ray microtomography. High-temperature rheology of enstatite: Implications for creep in the mantle. Numerical study of creep in two-phase aggregates with a large rheology contrast: Implications for the lower mantle. Crystal preferred orientations of garnet: Comparison between numerical simulations and electron back-scattered diffraction EBSD measurements in naturally deformed eclogites.

Plastic deformation of wadsleyite and olivine at high-pressure and high-temperature using a rotational Drickamer apparatus RDA. Fabric and elastic principal directions of cancellous bone are closely related. Phipps Morgan. Phase transformations and their bearing on the constitution and dynamics of the mantle.

Spontaneous small-scale melt segregation in partial melts undergoing deformation. Thermoelasticity of silicate perovskite and magnesiowustite and stratification of the Earth's mantle: Science. Flow in rocks modelled as multiphase continua: Application to polymineralic rocks. Average stress in the matrix and effective moduli of randomly oriented composites. Modelling the bulk viscosity of two-phase mixtures in terms of clast shape.

Effect of muscovite on the strength and lattice preferred orientations of experimentally deformed quartz aggregates. High-pressure X-ray tomography microscope: Synchrotron computed microtomography at high pressure and temperature. Evolution of olivine lattice preferred orientation during simple shear in the mantle. Some mineral physics constraints on the rheology and geothermal structure of Earth's lower mantle. Texture of Mg, Fe SiO3 perovskite and ferro-periclase aggregate: Implications for rheology of the lower mantle.

Very Good,No Highlights or Markup,all pages are intact. Vinogradov, The present book brings together these photographs for the first time. They are supported by a full explanatory text. Boger, K. Walters, The mathematical models are then tested using practical case studies. This book presents the evolution of the mathematical models used to calculate the resistance structures and the conditions which enable progress to be made in this field. Constantin Cristescu, Rao, This unique volume presents the scientific progress, state-of-art technology, and thrust areas to be focused in electrorheology ER and magentorheology MR.

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Collyer, D. Clegg, Rheology modifiers also known as thickeners or flow control agents are used for modifying the viscosity to meet the desired rheological profiles. There are Rheology Modifiers Organic and Inorganic Market …. Understanding the Rheological Characteristics of Thermoplastic …. Rheological testing of thermoplastic materials can be carried out on both melts and solid samples. Issues related to process ability can be correlated with By definition, fluid materials are systems which flow when subjected to stress. Analyzing how they respond to an input stress is the main objective of rheological

Under large deformation, bulk composite materials can undergo a transition . Complex density contrast was observed in the darker silicate regions .. In the normal mantle, the viscosity may be controlled by that of Pv if this.